Given: g(x) = f(x) cot(x) + kx, where k is a real number. f is differentiable for all x; f(7/4) = 2; f'(7π/4) = -4. (a) For what values of x, if any, in the interval 0 ≤ x < 2r will the derivative of g fail to exist? Justify your answer. Enter your answers as a Because cot(x) is undefined when x = and ? 2(x) is undefined when x = (b) If g k= values of x. = 9, find the value of k. comma-separated list. the derivative of g will fail to exist at these
Given: g(x) = f(x) cot(x) + kx, where k is a real number. f is differentiable for all x; f(7/4) = 2; f'(7π/4) = -4. (a) For what values of x, if any, in the interval 0 ≤ x < 2r will the derivative of g fail to exist? Justify your answer. Enter your answers as a Because cot(x) is undefined when x = and ? 2(x) is undefined when x = (b) If g k= values of x. = 9, find the value of k. comma-separated list. the derivative of g will fail to exist at these
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
Given: \( g(x) = f(x) \cdot \cot(x) + kx \), where \( k \) is a real number. \( f \) is differentiable for all \( x \); \( f\left(\frac{7\pi}{4}\right) = 2 \); \( f'\left(\frac{7\pi}{4}\right) = -4 \).
**(a)** For what values of \( x \), if any, in the interval \( 0 \leq x < 2\pi \) will the derivative of \( g \) fail to exist? Justify your answer. Enter your answers as a comma-separated list.
Because \( \cot(x) \) is undefined when \( x = \) [_______] and \( [?](x) \) is undefined when \( x = \) [_______], the derivative of \( g \) will fail to exist at these values of \( x \).
**(b)** If \( g\left(\frac{7\pi}{4}\right) = 9 \), find the value of \( k \).
\[ k = \, [\, __ \, ] \]
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Transcribed Image Text:**Problem Statement:**
Given: \( g(x) = f(x) \cdot \cot(x) + kx \), where \( k \) is a real number. \( f \) is differentiable for all \( x \); \( f\left(\frac{7\pi}{4}\right) = 2 \); \( f'\left(\frac{7\pi}{4}\right) = -4 \).
**(a)** For what values of \( x \), if any, in the interval \( 0 \leq x < 2\pi \) will the derivative of \( g \) fail to exist? Justify your answer. Enter your answers as a comma-separated list.
Because \( \cot(x) \) is undefined when \( x = \) [_______] and \( [?](x) \) is undefined when \( x = \) [_______], the derivative of \( g \) will fail to exist at these values of \( x \).
**(b)** If \( g\left(\frac{7\pi}{4}\right) = 9 \), find the value of \( k \).
\[ k = \, [\, __ \, ] \]
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Read It [Button]
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